Question

Find the weight of an object of mass 20 kg on the surface of a spherical planet whose mass and radius are twice of that of earth. ( g at the surface of earth = 10 m/s²)

Answer 1

$$\begin{gathered} \mathrm{Acceleration}\mathrm{due}\mathrm{to}\mathrm{gravity}: \\ \mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2} \\ \mathrm{Ratio}\mathrm{of}\mathrm{acceleration}\mathrm{due}\mathrm{to}\mathrm{gravity}: \\ \frac{{\mathrm{g}}_{\mathrm{planet}}}{{\mathrm{g}}_{\mathrm{earth}}}=\left[\frac{{\mathrm{M}}_2}{{\mathrm{M}}_1}\right]{\left[\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right]}^2 \\ =\left[\frac{2{\mathrm{M}}_1}{{\mathrm{M}}_1}\right]{\left[\frac{{\mathrm{R}}_1}{2{\mathrm{R}}_1}\right]}^2 \\ {\mathrm{g}}_{\mathrm{planet}}=10\times 2\times \frac{1}{4} \\ =5\mathrm{m}/{\mathrm{s}}^2 \\ \mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{object}\mathrm{on}\mathrm{mars}: \\ \mathrm{W}={\mathrm{mg}}_{\mathrm{planet}} \\ =20\times 5 \\ \mathbf{=}\mathbf{100}\mathbf{}\mathbf{N} \end{gathered}$$